u^2+u-1=0

Solution for u^2+u-1=0 equation:

Simplifying
u2 + u + -1 = 0

Reorder the terms:
-1 + u + u2 = 0

Solving
-1 + u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + u + 1 + u2 = 0 + 1

Reorder the terms:
-1 + 1 + u + u2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + u + u2 = 0 + 1
u + u2 = 0 + 1

Combine like terms: 0 + 1 = 1
u + u2 = 1

The u term is u.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
u + 0.25 + u2 = 1 + 0.25

Reorder the terms:
0.25 + u + u2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + u + u2 = 1.25

Factor a perfect square on the left side:
(u + 0.5)(u + 0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(u + 0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
u + 0.5 = 1.118033989

Simplifying
u + 0.5 = 1.118033989

Reorder the terms:
0.5 + u = 1.118033989

Solving
0.5 + u = 1.118033989

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + u = 1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + u = 1.118033989 + -0.5
u = 1.118033989 + -0.5

Combine like terms: 1.118033989 + -0.5 = 0.618033989
u = 0.618033989

Simplifying
u = 0.618033989

Subproblem 2
u + 0.5 = -1.118033989

Simplifying
u + 0.5 = -1.118033989

Reorder the terms:
0.5 + u = -1.118033989

Solving
0.5 + u = -1.118033989

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + u = -1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + u = -1.118033989 + -0.5
u = -1.118033989 + -0.5

Combine like terms: -1.118033989 + -0.5 = -1.618033989
u = -1.618033989

Simplifying
u = -1.618033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.618033989, -1.618033989}